There have been a small number of cases where it actually worked, but to my knowledge nothing universally applicable. AIDS treatments, however, have become so good that the disease is no longer seen as a major problem of our times.

We have a type of stem cell treatment used in extreme blood cancer situations that had cured a number of people of AIDS. To my understanding, it should work for most patients, but it's a risky and extreme enough procedure that it's not worthwhile compared to the standard treatment regimen. But if you also get leukemia, the treatment might cure both diseases.

Cancer is not one disease, at best you can cure a small specific subset of cancers.

With one given treatment, maybe. As far as I'm aware, there aren't any cancers that are in principle untreatable, though a handful are very difficult to cure people from. We have a wide variety of treatments for a wide variety of cancers, some of which are now really close to 100%.